April 12, 2018 Thursday
Bedtime Story
Note A of Ada Lovelace - Part 5
Tonight we are continuing with the Note A
of Ada Lovelace wherein she is now trying to explain how the Analytical
Machine, were it made to work, would carry out its operations.
“Now in the Analytical Engine, the
operations which come under the first of the above heads are ordered and
combined by means of a notation and of a train of mechanism which belong
exclusively to themselves; and with respect to the second head, whenever
numbers meaning operations and not quantities (such as the indices of powers)
are inscribed on any column or set of columns, those columns immediately act in
a wholly separate and independent manner, being connected with the operating
mechanism exclusively, and re-acting upon this.
They never come into combination with
numbers upon any other columns meaning quantities; though, of course, if there
are numbers meaning operations upon n columns, these may combine amongst each
other, and will often be required to do so, just as numbers meaning quantities
combine with each other in any variety.
It might have been arranged that all
numbers meaning operations should have appeared on some separate portion of the
engine from that which presents numerical quantities; but the present mode is
in some cases more simple, and offers in reality quite as much distinctness
when understood.
The operating mechanism can even be thrown
into action independently of any object to operate upon (although of course no
result could then be developed).
Again, it might act upon other things
besides number, were objects found whose mutual fundamental relations could be
expressed by those of the abstract science of operations, and which should be
also susceptible of adaptations to the action of the operating notation and
mechanism of the engine.
Supposing, for instance, that the
fundamental relations of pitched sounds in the science of harmony and of
musical composition were susceptible of such expressions and adaptations, the
engine might compose elaborate and scientific pieces of music of any degree of
complexity or extent.”
(Ada Lovelace had foreseen that a universal
Analytical Engine or a Universal computing machine would in principle be truly
capable of carrying out most complex audio and visual performances which today
not only does not surprise us but if today any computing device was unable to
do these tasks, we would frown and fume in disgust and anger.
There is field of mathematics known as
music theory which really has no axiomatic foundations in modern mathematics.
Yet, remarkably enough, musical sounds can
be described very accurately mathematically and in the words of Reginald
Brindle, a British composer ‘mathematics is the basis of sound and musical
sound exhibits a remarkable array of numerical properties simply because nature
itself is amazingly mathematical’ – Commentary of Pan narrans).
“The Analytical Engine is an embodying of
the science of operations, constructed with peculiar reference to abstract
number as the subject of these operations.
The Difference Engine is the embodying of
one particular and very limited set of operations, which may be expressed thus
(+, +, +, +, +, +), or thus, 6(+).
Six repetitions of the one operation, +,
is, in fact, the whole sum and object of that engine.”
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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